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Prove that: tan(pi/4+A). Tan((3pi)/4)+...

Prove that:
`tan(pi/4+A). Tan((3pi)/4)+A=-1`

Text Solution

Verified by Experts

LHS `=tan(pi/4+A).tan((3pi)/4+A)`
`=tan(pi/4+A).tan{pi/2+(pi/4+A)}`
`tan(pi/4+A).{-cot(pi/4+A)}`
`=-tan(pi/4+A).1/(tan(pi/4+A))`
`=-1`=RHS Hence proved.
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